On the supremum of γ-reflected processes with fractional Brownian motion as input
By Enkelejd Hashorva, Lanpeng Ji, V. Piterbarg. 2013
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Abstract Let { X H ( t ) , t ≥ 0 } be a fractional Brownian motion with Hurst index H ∈ ( 0 , 1 ] and define a γ -reflected process W γ ( t ) = X H ( t ) − c t − γ inf s ∈ [ 0 , t ] ( X H ( s ) − c s ) , t ≥ 0 with c > 0 , γ ∈ [ 0 , 1 ] two given constants. In this paper we establish the exact tail asymptotic behaviour of M γ ( T ) = sup t ∈ [ 0 , T ] W γ ( t ) for any T ∈ ( 0 , ∞ ] . Furthermore, we derive the exact tail asymptotic behaviour of the supremum of certain non-homogeneous mean-zero Gaussian random fields.
Subfields: Finance, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6f8498ad14ca812b3df6e9a9a1c6d9f5e30971ba
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In Finance
In Management Science and Operations Research
In Mathematical Physics
Citations in the corpus
- Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals (2013, background): “…risk models were studied for instance in Dȩbicki and Rolski (2002), where the finite-time ruin probability with 6 the choice Y (t) ≡ t was analyzed, whereas the infinite-time ruin counterpart was considered in Hüsler and Piterbarg (1999), see also the recent contribution Hashorva et al. (2013).”